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	ジョーンズ計算	ABCD行列	フーリエ光学
分野	光学	光学	光学
系統	Process / pipeline	Process / pipeline	Process / pipeline
提唱年	1941	1966	1822
提唱者	Robert Clark Jones	Herwig Kogelnik and Tingye Li	Joseph Fourier and Ernst Abbe
種類	Vector-matrix formalism	Ray optics formalism	Spectral decomposition method
原典	Jones, R. C. (1941). A new calculus for the treatment of optical systems: I. Description and discussion of the calculus. Journal of the Optical Society of America, 31(7), 488-493.	Kogelnik, H., & Li, T. (1966). Laser beams and resonators. Applied Optics, 5(10), 1550-1567.	Goodman, J. W. (1968). Introduction to Fourier Optics. McGraw-Hill.
別名	Jones vector method, Jones matrix, polarization calculus	ray transfer matrix, ABCD method, system matrix	frequency-domain optics, wave optics, diffraction theory
関連	3	3	3
概要	Jones calculus is a mathematical formalism for analyzing the propagation and manipulation of polarized light using vectors and matrices. Developed by Robert Clark Jones in 1941, it represents the electric field of a coherent optical beam as a two-component complex vector (Jones vector) and optical elements as matrices (Jones matrices), enabling elegant tracking of polarization through optical systems.	The ABCD matrix, or ray transfer matrix method, is a compact algebraic framework for analyzing optical systems. Introduced by Kogelnik and Li in 1966, it represents the linear transformation of ray position and angle (or Gaussian beam parameters) through optical elements. This method is foundational in laser physics, Gaussian optics, and optical design, enabling rapid calculation of resonator stability, beam propagation, and system performance.	Fourier optics is a mathematical framework that analyzes optical systems and phenomena using Fourier transforms and frequency-domain methods. Grounded in Joseph Fourier's 1822 work on heat diffusion and Ernst Abbe's microscopy theory, this approach decomposes optical fields into plane waves or spatial frequencies, revealing how optical systems manipulate and filter these components to produce images and transmit information.